German /r/ can be pronounced as /R/ (uvular trill), /ʁ/ (fricative), and in some accents /r/ (/r/ is not very common). There is probably not any logical distribution of regions with a uvular trill versus fricative as in French, as it seems to be in free variation in German (it is very obvious in some languages when the sound is a uvular trill versus fricative because the fricative can be devoiced to a voiceless uvular fricative /X/, whereas the trill is less likely to). The difference between /R/ and /ʁ/ is not really noticeable, because in all environments where /ʁ/ would be devoiced (e.g. at the coda of a syllable before a voiceless consonant) the /R/ or /ʁ/ becomes a totally different allophone. For example, the /R/ in "warten" is not even pronounced as /R/ because it occurs in coda position. If it were pronounced as /ʁ/ it would theoretically be devoiced, but because German does not allow coda /R/ or /ʁ/ it is almost impossible for phoneticians to know whether it is a trill or fricative just by listening. The sounds are very difficult to distinguish by the human ear (except maybe /R/ can be longer), and you really would to analyze a spectrogram to come up with a concrete conclusion, unless the speaker was exaggerating the sounds so that the difference was obvious.
Basically, both the trill and fricative work in onset position (not at the end of a syllable), and it is almost impossible for the human ear to distinguish. People with large uvula's probably make something which sounds more like /R/ because the uvula would flap around automatically while making frication noise. Just don't pronounce "r" as a trill or fricative at the end of a syllable.